Theorems · Theorem · measure theory
EuclideanSpace.volume_ball_fin_three
∀ (x : EuclideanSpace ℝ (Fin 3)) (r : ℝ), MeasureTheory.volume (Metric.ball x r) = ENNReal.ofReal r ^ 3 * ENNReal.ofReal (Real.pi * 4 / 3)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- mul_oneproof · cited by 3,885
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- pow_oneproof · cited by 894
- ENNReal.ofRealstatement and proof · cited by 863
- Metric.ballstatement · cited by 735
- EuclideanSpacestatement and proof · cited by 307
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanSpace.volume_closedBall_fin_threeproof · cited by 0